Higher regularizations for zeros of cuspidal automorphic L-functions of GL_d

TL;DR

This paper generalizes Milnor's regularized determinants to the zeros of cuspidal automorphic L-functions of GL_d over number fields, extending Deninger's work on the Riemann zeta function.

Contribution

It introduces higher depth analogues of regularized determinants for zeros of automorphic L-functions, broadening the scope of Milnor's and Deninger's frameworks.

Findings

Established higher depth regularized determinants for automorphic L-functions

Generalized Milnor's determinants to a broader class of L-functions

Extended Deninger's results from the Riemann zeta to GL_d automorphic cases

Abstract

We establish "higher depth" analogues of regularized determinants due to Milnor for zeros of cuspidal automorphic L-functions of GL_d over a general number field. This is a generalization of the result of Deninger about the regularized determinant for zeros of the Riemann zeta function.